Analysis of xx-top500-453-base.sdk
Contents
Original Sudoku
level: medium
position: .8.69....5......1...........3.7..8.....2.....1........4...15.........3.8....4.6.. initial
Autosolve
position: .8169.5.45..4.8.1..4.15..8..347618.5.5.2.41..1..5.94..46..15....159.6348....4.651 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 3,6 => CTR => C3: 2,7,9 * DIS # F3: 2,7 => CTR => F3: 3 * PRF # A3: 2,9 => SOL * DIS # A9: 2,9 => CTR => A9: 3,7,8 * DIS # C9: 3,8 => CTR => C9: 2,7,9 * DIS # A9: 2,7 => CTR => A9: 3,8,9 * DIS # A3: 2,7 => CTR => A3: 3,6,9 * DIS # C9: 3,8 => CTR => C9: 2,7,9 * DIS # A9: 2,7 => CTR => A9: 3,8,9 * DIS # F3: 2,7 => CTR => F3: 3 * CNT 10 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 3,6 => CTR => C3: 2,7,9 * DIS C3: 2,7,9 # F3: 2,7 => CTR => F3: 3 * PRF C3: 2,7,9 + F3: 3 # A3: 2,9 => SOL * STA C3: 2,7,9 + F3: 3 + A3: 2,9 * CNT 3 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.69....5......1...........3.7..8.....2.....1........4...15.........3.8....4.6.. | initial |
| .8169.5.45..4.8.1..4.15..8..347618.5.5.2.41..1..5.94..46..15....159.6348....4.651 | autosolve |
| 381692574526478913947153286234761895659284137178539462463815729715926348892347651 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C2: 3,6 E2: 2,7 I2: 3,6 A4: 2,9 B6: 2,7 E5: 3,8 E6: 3,8 H4: 2,9 C7: 3,8 A8: 2,7 D7: 3,8 E8: 2,7 D9: 3,8 F9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E8,F9: 2.. / E8 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) A4,H4: 2.. / A4 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) A8,E8: 2.. / A8 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) E2,E8: 2.. / E2 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) F1,F3: 3.. / F1 = 3 => 0 pairs (X) / F3 = 3 => 15 pairs (_) E5,E6: 3.. / E5 = 3 => 13 pairs (_) / E6 = 3 => 13 pairs (_) D7,D9: 3.. / D7 = 3 => 11 pairs (_) / D9 = 3 => 13 pairs (_) C2,I2: 3.. / C2 = 3 => 11 pairs (_) / I2 = 3 => 13 pairs (_) C7,D7: 3.. / C7 = 3 => 13 pairs (_) / D7 = 3 => 11 pairs (_) I2,I3: 6.. / I2 = 6 => 11 pairs (_) / I3 = 6 => 13 pairs (_) H5,H6: 6.. / H5 = 6 => 14 pairs (_) / H6 = 6 => 14 pairs (_) C2,I2: 6.. / C2 = 6 => 13 pairs (_) / I2 = 6 => 11 pairs (_) C6,H6: 6.. / C6 = 6 => 14 pairs (_) / H6 = 6 => 14 pairs (_) A3,A5: 6.. / A3 = 6 => 11 pairs (_) / A5 = 6 => 13 pairs (_) E8,F9: 7.. / E8 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) A8,E8: 7.. / A8 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) E2,E8: 7.. / E2 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) E5,E6: 8.. / E5 = 8 => 13 pairs (_) / E6 = 8 => 13 pairs (_) D7,D9: 8.. / D7 = 8 => 13 pairs (_) / D9 = 8 => 11 pairs (_) C6,E6: 8.. / C6 = 8 => 13 pairs (_) / E6 = 8 => 13 pairs (_) C7,D7: 8.. / C7 = 8 => 11 pairs (_) / D7 = 8 => 13 pairs (_) A5,A9: 8.. / A5 = 8 => 11 pairs (_) / A9 = 8 => 13 pairs (_) B2,G2: 9.. / B2 = 9 => 16 pairs (_) / G2 = 9 => 17 pairs (_) A4,H4: 9.. / A4 = 9 => 15 pairs (_) / H4 = 9 => 0 pairs (*) B2,B9: 9.. / B2 = 9 => 16 pairs (_) / B9 = 9 => 17 pairs (_) * DURATION: 0:00:49.773498 START: 18:13:01.248689 END: 18:13:51.022187 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B6,C2,C7,D7,D9,E2,E5,E6,E8,F9,H4,I2) * .8169.5.45..4.8.1..4.15..8..347618.5.5.2.41..1..5.94..46..15....159.6348....4.651 * PAIR C2: 3,6 BLK 1 A3: 3,6,2,7,9 # reduction candidate for 3,6 A3: 3,6 # 19 pairs C3: 3,6,2,7,9 # reduction candidate for 3,6 C3: 3,6 => CTR * .8169.5.45..4.8.1..4.15..8..347618.5.5.2.41..1..5.94..46..15....159.6348....4.651 C3: 2,7,9 # 14 pairs * PAIR E2: 2,7 BLK 2 F1: 2,7,3 # reduction candidate for 2,7 F1: 2,7 # 15 pairs F3: 2,7,3 # reduction candidate for 2,7 F3: 2,7 => CTR * 28169357457.428.1..4.15..8.934761825.572.41.912.5.94.746..15.92.159.6348....4.651 F3: 3 # 15 pairs * PAIR E2: 2,7 ROW 2 B2: 2,7,9 # reduction candidate for 2,7 B2: 2,7 # 17 pairs G2: 2,7,9 # reduction candidate for 2,7 G2: 2,7 # 16 pairs * PAIR I2: 3,6 BLK 3 I3: 3,6,2,7,9 # reduction candidate for 3,6 I3: 3,6 # 26 pairs I3: 2,7,9 # 11 pairs * PAIR A4: 2,9 COL A A3: 2,9,3,6,7 # reduction candidate for 2,9 A3: 2,9 => SOLVED * 381692574526478913947153286234761895659284137178539462463815729715926348892347651 A3: 3,6,7 # 14 pairs A9: 2,9,3,7,8 # reduction candidate for 2,9 A9: 2,9 => CTR * 38169.5.45..4.8.1.64.15..8..347618.585.2341..1..5894..46..15....159.6348....4.651 A9: 3,7,8 # 14 pairs * PAIR B6: 2,7 BLK 4 C6: 2,7,6,8 # reduction candidate for 2,7 C6: 6,8 # 18 pairs C6: 2,7 # 11 pairs * PAIR B6: 2,7 ROW 6 H6: 2,7,3,6 # reduction candidate for 2,7 H6: 2,7 # 14 pairs I6: 2,7,3 # reduction candidate for 2,7 I6: 2,7 # 20 pairs * PAIR B6: 2,7 COL B B2: 2,7,9 # reduction candidate for 2,7 B2: 2,7 # 17 pairs B9: 2,7,9 # reduction candidate for 2,7 B9: 2,7 # 16 pairs * PAIR H4: 2,9 COL H H7: 2,9,7 # reduction candidate for 2,9 H7: 7 # 18 pairs H7: 2,9 # 16 pairs * PAIR C7: 3,8 BLK 7 A9: 3,8,2,7,9 # reduction candidate for 3,8 A9: 3,8 # 15 pairs C9: 3,8,2,7,9 # reduction candidate for 3,8 C9: 3,8 => CTR * .8169.5.45..4.8.1..4.15..8..347618.5.5.2.41..1..5.94..46..15....159.6348....4.651 C9: 2,7,9 # 15 pairs * PAIR A8: 2,7 BLK 7 A9: 2,7,3,8,9 # reduction candidate for 2,7 A9: 2,7 => CTR * 38169.5.45..4.8.1.64.15..8.93476182585.2341..1..5894..46..15....159.6348....4.651 A9: 3,8,9 # 14 pairs B9: 2,7,9 # reduction candidate for 2,7 B9: 2,7 # 16 pairs C9: 2,7,3,8,9 # reduction candidate for 2,7 C9: 2,7 # 19 pairs * PAIR A8: 2,7 COL A A1: 2,7,3 # reduction candidate for 2,7 A1: 2,7 # 19 pairs A3: 2,7,3,6,9 # reduction candidate for 2,7 A3: 2,7 => CTR * 3816925745.6478.13.4.153.8693476182565728413912853946746381579271592634889.34.651 A3: 3,6,9 # 14 pairs * PAIR D9: 3,8 ROW 9 A9: 3,8,2,7,9 # reduction candidate for 3,8 A9: 3,8 # 15 pairs C9: 3,8,2,7,9 # reduction candidate for 3,8 C9: 3,8 => CTR * .8169.5.45..4.8.1..4.15..8..347618.5.5.2.41..1..5.94..46..15....159.6348....4.651 C9: 2,7,9 # 15 pairs * PAIR F9: 2,7 ROW 9 A9: 2,7,3,8,9 # reduction candidate for 2,7 A9: 2,7 => CTR * 38169.5.45..4.8.1.64.15..8.93476182585.2341..1..5894..46..15....159.6348....4.651 A9: 3,8,9 # 14 pairs B9: 2,7,9 # reduction candidate for 2,7 B9: 2,7 # 16 pairs C9: 2,7,3,8,9 # reduction candidate for 2,7 C9: 2,7 # 19 pairs * PAIR F9: 2,7 COL F F1: 2,7,3 # reduction candidate for 2,7 F1: 2,7 # 15 pairs F3: 2,7,3 # reduction candidate for 2,7 F3: 2,7 => CTR * 28169357457.428.1..4.15..8.934761825.572.41.912.5.94.746..15.92.159.6348....4.651 F3: 3 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-453-base-pr-000.dot * REASONING * DIS # C3: 3,6 => CTR => C3: 2,7,9 * DIS # F3: 2,7 => CTR => F3: 3 * PRF # A3: 2,9 => SOL * DIS # A9: 2,9 => CTR => A9: 3,7,8 * DIS # C9: 3,8 => CTR => C9: 2,7,9 * DIS # A9: 2,7 => CTR => A9: 3,8,9 * DIS # A3: 2,7 => CTR => A3: 3,6,9 * DIS # C9: 3,8 => CTR => C9: 2,7,9 * DIS # A9: 2,7 => CTR => A9: 3,8,9 * DIS # F3: 2,7 => CTR => F3: 3 * CNT 10 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B6,C2,C7,D7,D9,E2,E5,E6,E8,F9,H4,I2) * .8169.5.45..4.8.1..4.15..8..347618.5.5.2.41..1..5.94..46..15....159.6348....4.651 * PAIR C2: 3,6 BLK 1 A3: 3,6,2,7,9 # reduction candidate for 3,6 A3: 3,6 # 19 pairs C3: 3,6,2,7,9 # reduction candidate for 3,6 C3: 3,6 => CTR * .8169.5.45..4.8.1..4.15..8..347618.5.5.2.41..1..5.94..46..15....159.6348....4.651 * RESTART * PAIR C2: 3,6 BLK 1 A3: 3,6,2,7,9 # reduction candidate for 3,6 A3: 3,6 # 19 pairs A3: 2,7,9 # 14 pairs * PAIR E2: 2,7 BLK 2 F1: 2,7,3 # reduction candidate for 2,7 F1: 2,7 # 15 pairs F3: 2,7,3 # reduction candidate for 2,7 F3: 2,7 => CTR * 28169357457.428.1..4.15..8.934761825.572.41.912.5.94.746..15.92.159.6348....4.651 * RESTART * PAIR E2: 2,7 ROW 2 B2: 2,7,9 # reduction candidate for 2,7 B2: 2,7 # 18 pairs G2: 2,7,9 # reduction candidate for 2,7 G2: 2,7 # 18 pairs * PAIR A4: 2,9 COL A A3: 2,9,6,7 # reduction candidate for 2,9 A3: 2,9 => SOLVED * 381692574526478913947153286234761895659284137178539462463815729715926348892347651 * DURATION: 0:00:10.746597 START: 18:14:32.067939 END: 18:14:42.814536 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-453-base-pr-001.dot * REASONING * DIS # C3: 3,6 => CTR => C3: 2,7,9 * DIS C3: 2,7,9 # F3: 2,7 => CTR => F3: 3 * PRF C3: 2,7,9 + F3: 3 # A3: 2,9 => SOL * STA C3: 2,7,9 + F3: 3 + A3: 2,9 * CNT 3 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 453 solution: 381692574526478913947153286234761895659284137178539462463815729715926348892347651 info: 95454 FNBHYK S8.f 23843 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 381692574526478913947153286234761895659284137178539462463815729715926348892347651 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* INC # A3: 3,6 => UNS * DIS # C3: 3,6 => CTR => C3: 2,7,9 * INC # C3: 2,7,9 => UNS * INC # F1: 2,7 => UNS * DIS # F3: 2,7 => CTR => F3: 3 * INC # F3: 3 => UNS * INC # B2: 2,7 => UNS * INC # G2: 2,7 => UNS * INC # I3: 3,6 => UNS * INC # I3: 2,7,9 => UNS * PRF # A3: 2,9 => SOL * INC # A3: 3,6,7 => UNS * DIS # A9: 2,9 => CTR => A9: 3,7,8 * INC # A9: 3,7,8 => UNS * INC # C6: 2,7 => UNS * INC # C6: 6,8 => UNS * INC # H6: 2,7 => UNS * INC # I6: 2,7 => UNS * INC # B2: 2,7 => UNS * INC # B9: 2,7 => UNS * INC # H7: 2,9 => UNS * INC # H7: 7 => UNS * INC # A9: 3,8 => UNS * DIS # C9: 3,8 => CTR => C9: 2,7,9 * INC # C9: 2,7,9 => UNS * DIS # A9: 2,7 => CTR => A9: 3,8,9 * INC # A9: 3,8,9 => UNS * INC # B9: 2,7 => UNS * INC # C9: 2,7 => UNS * INC # A1: 2,7 => UNS * DIS # A3: 2,7 => CTR => A3: 3,6,9 * INC # A3: 3,6,9 => UNS * INC # A9: 3,8 => UNS * DIS # C9: 3,8 => CTR => C9: 2,7,9 * INC # C9: 2,7,9 => UNS * DIS # A9: 2,7 => CTR => A9: 3,8,9 * INC # A9: 3,8,9 => UNS * INC # B9: 2,7 => UNS * INC # C9: 2,7 => UNS * INC # F1: 2,7 => UNS * DIS # F3: 2,7 => CTR => F3: 3 * INC # F3: 3 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 3,6 => UNS * DIS # C3: 3,6 => CTR => C3: 2,7,9 * INC C3: 2,7,9 # A3: 3,6 => UNS * INC C3: 2,7,9 # A3: 2,7,9 => UNS * INC C3: 2,7,9 # F1: 2,7 => UNS * DIS C3: 2,7,9 # F3: 2,7 => CTR => F3: 3 * INC C3: 2,7,9 + F3: 3 # B2: 2,7 => UNS * INC C3: 2,7,9 + F3: 3 # G2: 2,7 => UNS * PRF C3: 2,7,9 + F3: 3 # A3: 2,9 => SOL * STA C3: 2,7,9 + F3: 3 + A3: 2,9 * CNT 9 HDP CHAINS / 9 HYP OPENED